Episode 33 - Why the floor holds you up

Tomlin Hawthorne

Stamp your foot on the floor. Go on.

Tomlin Hawthorne

Your foot stopped. Of course it stopped. The floor's solid.

Tomlin Hawthorne

But think about what we've learned. An atom is a cathedral with a fly in it. The nucleus is the fly. The rest is, on the face of it, nothing. Your foot is made of atoms. So is the floor. Two great stretches of emptiness, each with a few specks in it.

Tomlin Hawthorne

So when the nothing of your foot met the nothing of the floor, what stopped it?

Tomlin Hawthorne

If you said the electrons repel each other, that's a good try, and it's not the answer. Electric repulsion alone wouldn't do it. Atoms are neutral overall, and by the old physics, matter squeezed hard enough would simply collapse into itself.

Tomlin Hawthorne

The real reason is a rule discovered in 1925 by a twenty-four-year-old with a famously sharp tongue. It's a rule with no cause that anyone can point to. It isn't a force. It's more like a law of etiquette among electrons. And without it there'd be no chemistry, no solids, no you. Today's question: if atoms are mostly empty, why is anything solid?

Tomlin Hawthorne

Last time, I asked you to pick one of the five readings of quantum mechanics and defend it against a friend, and then swap. I hope it got heated. And I hope you found, as people often do, that the one you were made to defend against your will turned out to have more going for it than you expected.

Tomlin Hawthorne

After three episodes of that, you've earned something concrete. Today there's no mystery about what's real. Today quantum mechanics rolls up its sleeves and explains the kitchen table.

Tomlin Hawthorne

Let me start with a book, and it's one of the great books of the last century.

Tomlin Hawthorne

Primo Levi was a chemist from Turin. In 1944, at twenty-four, he was deported to Auschwitz. He survived, in part, because the camp needed chemists for a synthetic rubber plant. He went home, worked for thirty years as the manager of a paint factory, and wrote.

Tomlin Hawthorne

In 1975 he published a book called The Periodic Table. It has twenty-one chapters, and each is named after an element. Argon is about his ancestors, the Jews of Piedmont, who he says were like the inert gases: noble, and inclined to keep to themselves. Iron is about a friend who taught him to climb mountains, and who was later killed by the Fascists. Cerium is about the camp, where he stole small rods of the stuff from the laboratory, filed them down in secret at night, and traded them as cigarette-lighter flints for bread. That bread kept him and a friend alive for the last two months.

Tomlin Hawthorne

And the final chapter is Carbon. It follows a single atom of carbon. It's locked in limestone for hundreds of millions of years. A man with a pickaxe frees it. It's roasted in a kiln, and flies off as carbon dioxide. It's breathed in by a falcon, dissolved in the sea, caught by a leaf and built into a sugar. It's drunk in a glass of wine. And at the very end, it enters a cell in the author's own brain, and takes part in the decision to put down, on the page, the full stop that ends the book.

Tomlin Hawthorne

I can't think of a better demonstration that chemistry is a way of seeing. And what Levi was looking at, that table, with its rows and columns, is today's subject. Because for sixty years nobody knew why it has the shape it does.

Tomlin Hawthorne

St Petersburg, February 1869. Dmitri Mendeleev is a professor of chemistry, thirty-five, a Siberian, the youngest of at least fourteen children, with a vast beard and hair that he had cut once a year. He's writing a textbook, and he's stuck on how to organise the chapters. There are sixty-three known elements, and no system to them.

Tomlin Hawthorne

He wrote each element on a card, with its weight and its properties. And, the story goes, he laid them out like a game of patience, which he liked to play on long train journeys. In order of weight, left to right, starting a new row whenever the properties began to repeat.

Tomlin Hawthorne

And they did repeat. Go along by weight, and every so often you come back to a soft metal that fizzes violently in water. Lithium. Then, seven places on, sodium. Then potassium. Stack the rows, and those three line up in a column. So do the elements next to them. The properties of the elements are periodic: they come round again, like the days of the week.

Tomlin Hawthorne

Others had half-noticed this. What made Mendeleev great was his nerve. Where the pattern didn't quite work, he didn't bend the pattern. He said the facts were wrong. If an element didn't fit its place, he declared that its weight had been measured badly. And where there was no element to fit, he left a gap, and said: there is an element here that hasn't been found yet.

Tomlin Hawthorne

And then he described them. He picked three gaps and predicted, in detail, what would be found. For the one below aluminium, which he called eka-aluminium, he gave its weight, said it would be a metal that melts in your hand, and said its density would be about six times that of water.

Tomlin Hawthorne

Six years later a French chemist discovered a new metal by its spectral lines, that barcode again, and named it gallium, after France. It melts in your hand. He measured its density as four point seven.

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Mendeleev, who'd never seen the stuff, wrote to Paris to tell him he'd got it wrong. Your sample must be impure. Measure it again.

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The Frenchman, not pleased, purified it and measured again. Five point nine.

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That's a man who trusted a pattern over a measurement, and was right. All three of his gaps were filled within fifteen years.

Tomlin Hawthorne

But he had no idea why the pattern exists. Why should the properties repeat? Why after eight, and then eight again, and then eighteen? It was a set of dance steps with no music.

Tomlin Hawthorne

The music was supplied by Wolfgang Pauli.

Tomlin Hawthorne

Pauli was born in Vienna in 1900. His godfather was Ernst Mach, the man who didn't believe in atoms. At twenty he wrote an account of Einstein's relativity so masterly that Einstein said he could hardly believe it was by someone so young. He was short, round, rocked back and forth while he thought, and was the most feared critic in physics. He's the source of the best insult in science. Shown a paper by a young colleague, he's said to have remarked, sadly: this isn't right. It isn't even wrong.

Tomlin Hawthorne

He was also notorious for something his colleagues called the Pauli effect. Experiments failed when he was nearby. Equipment broke. One laboratory in Göttingen suffered a mysterious explosion and then discovered that Pauli's train had been standing in the station at the time. A friend, an experimenter, banned him from the building. They were only half joking.

Tomlin Hawthorne

In 1925, he was puzzling over the atom. By then, thanks to Bohr and the rest, it was known that an electron in an atom can only be in certain states, the standing-wave patterns from episode twenty-eight. The rungs of the ladder.

Tomlin Hawthorne

So here's a question. Take a big atom, like gold, with seventy-nine electrons. Everything in nature tends to settle to its lowest energy. So why don't all seventy-nine electrons just drop to the bottom rung and sit there together?

Tomlin Hawthorne

If they did, every atom would be a tiny, tight ball, all much alike. There'd be no difference worth speaking of between gold and oxygen and carbon. No chemistry at all.

Tomlin Hawthorne

Pauli's answer was a new law. He called it the exclusion principle. No two electrons can be in the same state. Ever.

Tomlin Hawthorne

That's it. Each available state can hold one electron and no more. It's occupied, or it isn't.

Tomlin Hawthorne

I'll qualify that in one small way. An electron has an extra property called spin, which can point one of two ways. So each wave pattern can actually hold two electrons, one of each spin. But those count as different states. The rule stands: one state, one electron.

Tomlin Hawthorne

Think of a theatre filling up. The best seats are in the front row. The first people in take them. Once the front row is full, the next arrivals can't sit there, however much they'd like to. They have to go to the second row. Then the third. The audience fills from the front, row by row, each person in the best seat still free.

Tomlin Hawthorne

Electrons in an atom do exactly that. The lowest pattern takes two. That's full. The next group of patterns takes eight. Then eight more. Then eighteen.

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Two, eight, eight, eighteen.

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Those are the lengths of the rows of the periodic table.

Tomlin Hawthorne

That's the answer to Mendeleev's riddle. The rows of his chart are the rows of the theatre. Each time a row fills up and a new one starts, you get an element with the same arrangement of electrons on the outside as the one above it. And it's the outside electrons that do the chemistry, because those are the ones that meet other atoms.

Tomlin Hawthorne

So the periodic table isn't just a filing system. It's a picture of the solutions to Schrödinger's equation for an electron bound to a nucleus, stacked up according to Pauli's rule. The thing on the classroom wall is a diagram of quantum mechanics.

Tomlin Hawthorne

Let me show you how much it explains.

Tomlin Hawthorne

Take an atom whose outer row is exactly full. Every seat taken, none over. It has no reason to gain an electron or lose one. It doesn't react with anything. Those are the inert gases: helium, neon, argon. Levi's aloof ancestors.

Tomlin Hawthorne

Now take an atom with one electron more than a full row. That one electron is on its own, out in a new row, far from the nucleus, loosely held. The atom gives it up very easily. That's lithium, sodium, potassium: the soft metals that go off like fireworks in water.

Tomlin Hawthorne

And an atom with one electron fewer than a full row. One empty seat. It'll grab an electron from anything nearby to fill it. That's fluorine and chlorine: savage, corrosive, poisonous.

Tomlin Hawthorne

Now put sodium next to chlorine. One has an electron it's keen to lose. The other has a gap it's desperate to fill. The electron hops across. Now the sodium is positively charged and the chlorine is negatively charged, and they cling together.

Tomlin Hawthorne

A metal that explodes in water, and a poison gas that was used as a weapon in the First World War. Put them together, and you sprinkle the result on your chips. All of chemistry is like that. It's electrons, looking for a comfortable seat.

Tomlin Hawthorne

Now. The floor.

Tomlin Hawthorne

When you stamp, the atoms of your shoe are pushed against the atoms of the floor. Their electron clouds start to overlap.

Tomlin Hawthorne

And Pauli's rule says: the electrons in your shoe can't go into the states already occupied by the electrons in the floor. Those seats are taken. If you want to force them into the same region, they'll have to go up into higher, empty states. And that costs energy. A lot. The harder you push, the more it costs.

Tomlin Hawthorne

That's what you feel as solidity. It isn't electric repulsion, mainly. It's exclusion. Combined with the thing from episode thirty: squeeze an electron into a smaller space, and by the uncertainty principle it moves more violently, and pushes back.

Tomlin Hawthorne

So you've never touched anything. Not in the sense you imagine. When your hand rests on a table, no part of you is in contact with any part of it. The electrons of your skin and the electrons of the wood are declining to share a state. What you feel as the firm surface of the world is a rule of quantum mechanics being enforced.

Tomlin Hawthorne

And it took a long time to be sure of that. It wasn't until 1967 that two mathematical physicists, Freeman Dyson and Andrew Lenard, actually proved it. If electrons didn't obey Pauli's principle, ordinary matter would be unstable. Two lumps of it brought together would merge and shrink, releasing an explosion of energy. The exclusion principle is all that stands between you and that.

Tomlin Hawthorne

I should correct something I said at the start, while I'm here. I called the atom empty. That's the picture from Rutherford, and by now you can see what's wrong with it. The electron isn't a speck rattling about in a void. It's a wave, and the wave fills the atom. The atom isn't empty. It's full of electron. That's why it takes up room.

Tomlin Hawthorne

The same rule holds up stars. When a star like the Sun runs out of fuel, gravity crushes it down until it's about the size of the Earth. And there it stops. What stops it is Pauli. The electrons are jammed together so tightly that every low state is taken, and gravity can't force them any closer. That's a white dwarf: a star held up by etiquette.

Tomlin Hawthorne

Unless it's too heavy. That's what Chandrasekhar worked out on the boat, in episode twenty-six. Above a certain mass, even exclusion gives way. The electrons are driven into the protons, and you get a ball of neutrons, ten miles across, with a teaspoon of it weighing a billion tonnes. Neutrons obey Pauli's rule too, and they hold. Unless the star is heavier still. And then nothing holds, and you get a black hole.

Tomlin Hawthorne

One last thing, and it sets up the next episode.

Tomlin Hawthorne

Not every kind of particle obeys the exclusion principle. It turns out there are two great tribes.

Tomlin Hawthorne

One tribe is called fermions, after Enrico Fermi. Electrons are fermions. So are the protons and neutrons in the nucleus. They're the antisocial ones. No two in the same state. And because they can't pile up, they take up space. Fermions are what stuff is made of.

Tomlin Hawthorne

The other tribe is called bosons, after an Indian physicist, Satyendra Nath Bose. Photons are bosons. And bosons are the opposite. They're gregarious. Not only can any number of them share a state. They prefer to. The more there are in a state already, the more likely the next one is to join.

Tomlin Hawthorne

Get an enormous number of photons into exactly the same state, all the same colour, all in step, all going the same way, and you have a laser.

Tomlin Hawthorne

So: matter, which is solid and stays out of its own way, and light, which passes through itself and piles up. The difference between a brick and a sunbeam comes down to whether the particles are willing to sit in each other's laps.

Tomlin Hawthorne

The myth of the week is the one I just corrected in myself: that atoms are ninety-nine point nine per cent empty space, and that if you took the space out of every person on Earth, the human race would fit in a sugar cube.

Tomlin Hawthorne

The arithmetic of the sugar cube is roughly right, if you mean the nuclei. But the picture's wrong. That space isn't empty. It's occupied by electron waves, which have every right to be there and can't be removed. You can't take the space out of an atom any more than you can take the vibration out of a note.

Tomlin Hawthorne

And the question to take away.

Tomlin Hawthorne

I've just explained the periodic table, and with it, in principle, the whole of chemistry, using two ideas from physics: standing waves and the exclusion principle. So is chemistry just physics? Applied physics, with messier sums?

Tomlin Hawthorne

Paul Dirac thought so. In 1929 he wrote that the laws needed for the whole of chemistry were now completely known, and the only difficulty was that the equations were too hard to solve.

Tomlin Hawthorne

Chemists were not charmed. And they have a point. Could you really start from Schrödinger's equation and work out the smell of coffee? The colour of a rose? What Primo Levi saw when he looked at a varnish that wouldn't set? In practice, no. Not remotely. Chemists have their own concepts, bonds, acids, catalysts, that don't appear anywhere in the physics and that they couldn't do without.

Tomlin Hawthorne

So is chemistry reducible to physics, or isn't it? Hold on to that. It comes back in episode forty-nine, and by then we'll be asking it about you.

Tomlin Hawthorne

Your challenge. Two parts.

Tomlin Hawthorne

One. Find a periodic table. There's one a few seconds away on any phone. Look at the far left column, under hydrogen: lithium, sodium, potassium, and below them rubidium and caesium. You know what sodium does in water. Predict what caesium does. Then find a video. Do the same with the column on the far right, and the column next to it.

Tomlin Hawthorne

You're doing what Mendeleev did. Reading a property off a position.

Tomlin Hawthorne

Two. Put your palm flat on a table and press. And describe to yourself what's happening, in the terms we've used today. Not: the table is hard. What are the electrons doing?

Tomlin Hawthorne

And read the last chapter of Levi's book. It's ten pages.

Tomlin Hawthorne

Next time, the last episode of Part Six. We've spent seven weeks on how strange this theory is. So let's ask where it is. The answer is that you're holding it. And we'll find out what a quantum computer does, and doesn't, and why hardly anything you've read about them is right.